Measures of lack of fit from tests of chi-squared type |
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Authors: | David S. Moore |
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Affiliation: | Department of Statistics, Purdue University, West Lafayette, IN 47907, USA |
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Abstract: | If X2 is the Pearson chi-squared statistic for testing fit, then has long been considered an associated measure of the degree of lack of fit. Here we consider two classes of statistics of chi-squared type, each having X2 as a member. The first is a class of directed divergence statistics discussed by Cressie and Read, the second consists of nonnegative definite quadratic forms in the standardized cell frequencies. We investigate the large sample behavior of , where T is any of these statistics. A number of auxiliary results on the Cressie-Read statistics are also obtained. The measures are illustrated by application to data from classical physics compiled by Stigler. |
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Keywords: | 62G10 Goodness of fit Minimum discrepancy estimators Pearson statistic |
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